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April 2018 Detecting rare and faint signals via thresholding maximum likelihood estimators
Yumou Qiu, Song Xi Chen, Dan Nettleton
Ann. Statist. 46(2): 895-923 (April 2018). DOI: 10.1214/17-AOS1574

Abstract

Motivated by the analysis of RNA sequencing (RNA-seq) data for genes differentially expressed across multiple conditions, we consider detecting rare and faint signals in high-dimensional response variables. We address the signal detection problem under a general framework, which includes generalized linear models for count-valued responses as special cases. We propose a test statistic that carries out a multi-level thresholding on maximum likelihood estimators (MLEs) of the signals, based on a new Cramér-type moderate deviation result for multidimensional MLEs. Based on the multi-level thresholding test, a multiple testing procedure is proposed for signal identification. Numerical simulations and a case study on maize RNA-seq data are conducted to demonstrate the effectiveness of the proposed approaches on signal detection and identification.

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Yumou Qiu. Song Xi Chen. Dan Nettleton. "Detecting rare and faint signals via thresholding maximum likelihood estimators." Ann. Statist. 46 (2) 895 - 923, April 2018. https://doi.org/10.1214/17-AOS1574

Information

Received: 1 August 2016; Revised: 1 April 2017; Published: April 2018
First available in Project Euclid: 3 April 2018

zbMATH: 06870283
MathSciNet: MR3782388
Digital Object Identifier: 10.1214/17-AOS1574

Subjects:
Primary: 62H15
Secondary: 62G20 , 62G32

Keywords: Detection boundary , false discovery proportion , generalized linear model , Moderate deviation , multiple testing procedure , RNA-seq data

Rights: Copyright © 2018 Institute of Mathematical Statistics

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Vol.46 • No. 2 • April 2018
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